DIVIDE: A Framework for Learning from Independent Multi-Mechanism Data Using Deep Encoders and Gaussian Processes

TL;DR

DIVIDE is a novel framework that disentangles multiple independent mechanisms in scientific data using deep encoders and Gaussian Processes, enabling interpretable predictions and active learning.

Contribution

It introduces a joint latent space model combining mechanism-specific deep encoders with structured Gaussian Processes for disentangling independent data mechanisms.

Findings

Successfully separates mechanisms in synthetic and real datasets

Reproduces additive and scaled interactions accurately

Remains robust under noisy conditions

Abstract

Scientific datasets often arise from multiple independent mechanisms such as spatial, categorical or structural effects, whose combined influence obscures their individual contributions. We introduce DIVIDE, a framework that disentangles these influences by integrating mechanism-specific deep encoders with a structured Gaussian Process in a joint latent space. Disentanglement here refers to separating independently acting generative factors. The encoders isolate distinct mechanisms while the Gaussian Process captures their combined effect with calibrated uncertainty. The architecture supports structured priors, enabling interpretable and mechanism-aware prediction as well as efficient active learning. DIVIDE is demonstrated on synthetic datasets combining categorical image patches with nonlinear spatial fields, on FerroSIM spin lattice simulations of ferroelectric patterns, and on experimental PFM hysteresis loops from PbTiO3 films. Across benchmarks, DIVIDE separates mechanisms, reproduces additive and scaled interactions, and remains robust under noise. The framework extends naturally to multifunctional datasets where mechanical, electromagnetic or optical responses coexist.